(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The 3 kg collar B slides on the frictionless arm AA'. The arm is attached to drum D and rotates about O in a horizontal plane at the rate dθ/dt = 0.75t, where dθ/dt and t are expressed in rad/s and seconds, respectively. As the arm-drum assembly rotates, a mechanism within the drum releases cord so that the collar moves outward from O with a constant speed of 0.5 m/s. Knowing that at t = 0, r = 0, determine the time at which the tension in the cord is equal to the magnitude of the horizontal force exerted on B by arm AA'.

2. Relevant equations

F_{r}= m(d^{2}θ/dt^{2}- r(dθ/dt)^{2})

F_{θ}= m(rd^{2}θ/dt^{2}+ 2(dr/dt)(dθ/dt))

ƩF = ma

3. The attempt at a solution

F_{r}= -T

r = (0.5 m/s)t

dr/dt = 0.5 m/s

d^{2}r/dt = 0 m/s^{2}

dθ/dt = (0.75 m/s)t

d^{2}θ/dt = 0.75 m/s^{2}

F_{r}= 3 kg(0 - 0.5t(0.75t)^{2})

F_{r}= -0.844t^{3}

F_{θ}= 3 kg(0.5t(.75) + 2(0.5)(0.75t))

F_{θ}= 3.375t

Now if F_{r}= -T then I can substitute -T for F_{r}. Therefore

T = 0.844t^{3}

I'm not sure where to go after this one.. I need to somehow solve for t I know that but I'm just not sure because I have two equations and three unknowns.

Thanks ahead of time for any help.

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# Radial and Transverse Forces Beer and Johnston 9th ed. 12.70

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